%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET594+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:32:50 AM UTC 2026
% Result : Theorem 12.60s 1.95s
% Output : CNFRefutation 12.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 53 ( 5 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 40 ( 12 ~; 21 |; 1 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 3 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(union_defn,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ) ).
fof(intersection_defn,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
fof(commutativity_of_union,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0) ).
fof(prove_th53,conjecture,
! [X0,X1,X2] :
( union(intersection(X0,X1),intersection(X0,X2)) = X0
=> subset(X0,union(X1,X2)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( union(intersection(X0,X1),intersection(X0,X2)) = X0
=> subset(X0,union(X1,X2)) ),
inference(negate_conjecture,[status(cth)],[prove_th53]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c2,plain,
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c3,plain,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c4,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c5,plain,
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c7,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c12,plain,
union(X0,X1) = union(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_union]) ).
cnf(c21,plain,
union(intersection(sK21,sK22),intersection(sK21,sK23)) = sK21,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c22,plain,
~ subset(sK21,union(sK22,sK23)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset(X0,union(X1,X2))
| ~ member(sK3(X0,union(X1,X2)),X2) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d1,plain,
( member(X0,intersection(sK21,sK22))
| member(X0,intersection(sK21,sK23))
| ~ member(X0,sK21) ),
inference(superposition,[status(thm)],[c21,c3]) ).
cnf(d2,plain,
( ~ member(X0,sK21)
| member(X0,intersection(sK21,sK22))
| member(X0,sK23) ),
inference(resolution,[status(thm)],[c7,d1]) ).
cnf(d3,plain,
( member(X0,sK22)
| member(X0,sK23)
| ~ member(X0,sK21) ),
inference(resolution,[status(thm)],[d2,c7]) ).
cnf(d4,plain,
( subset(sK21,X0)
| member(sK3(sK21,X0),sK23)
| member(sK3(sK21,X0),sK22) ),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
( subset(X0,union(X1,X2))
| ~ member(sK3(X0,union(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d6,plain,
( member(sK3(sK21,union(sK23,X0)),sK22)
| subset(sK21,union(sK23,X0))
| subset(sK21,union(sK23,X0)) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( subset(sK21,union(sK23,sK22))
| subset(sK21,union(sK23,sK22)) ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
subset(sK21,union(sK22,sK23)),
inference(demodulation,[status(thm)],[d7,c12]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c22,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET594+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:58:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.60/1.95 % SZS status Theorem for theBenchmark.p
% 12.60/1.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------